A common prediction task is to estimate a function ƒ from predictors to target domain (sometimes referred to as a score). This estimation can be determined, for example, using a linear regression model which is a linear combination of predictors:
      f    =                  w        0            +                        ∑                      i            =            1                    I                ⁢                              w            i                    ⁢                      x            i                                ,                where xi is the value of the ith predictor, and wi the regression weight to be trained.        
Compared with regression models, scorecard models include a binning step to divide each predictor space into bins, and then assign score weight to each bin.
      f    =                  w        0            +                        ∑                      i            =            1                    I                ⁢                              f            i                    ⁡                      (                          x              i                        )                                ,                where ƒi(xi) is the predictor score:        
            f      i        ⁡          (              x        i            )        =            ∑              j        =        1                    J        i              ⁢                  w        ij            ⁢                        b          ij                ⁡                  (                      x            i                    )                                    wij: the score weights associated with bin j for predictor xi.        bij: the dummy indicator variables for the bins of predictor xi.        
            b      ij        ⁡          (              x        i            )        =      {                            1                                      if            ⁢                                                  ⁢            value            ⁢                                                  ⁢            of            ⁢                                                  ⁢                          x              i                        ⁢                                                  ⁢            belongs            ⁢                                                  ⁢            to            ⁢                                                  ⁢            the            ⁢                                                  ⁢            jth            ⁢                                                  ⁢            bin                                                0                          else                    
Bins for all predictors can be generated using various binning algorithms, which also support categorical predictors. Missing values can be handled using a missing value bin. Given enough bins for a predictor xi, the above predictor score function ƒi(xi) is flexible to approximate any general function based on a single predictor, and the scorecard model is the sum of such functions. The complete, compact representation of a model by its bin definitions and weights makes the scorecard a popular, transparent, and easily understood model formulation. And the ability of a scorecard to approximate general functions makes it a strong predictive tool.
A scorecard model can be trained to optimize the bin weights such that the prediction error for the model is minimized. Scorecards can be used to predict both continuous and binary targets. Scorecards are generally characterized as being much more powerful than regression models, and still simple enough to be interpretable. By looking into the bin weights for the predictors, insight can be gained for the data.